Polygonal non-wetting droplets on microtextured surfaces

Understanding the interactions between liquids and solids is important for many areas of science and technology. Microtextured surfaces have been extensively studied in microfluidics, DNA technologies, and micro-manufacturing. For these applications, the ability to precisely control the shape, size and location of the liquid via textured surfaces is of particular importance for the design of fluidic-based systems. However, this has been passively realized in the wetting state thanks to the pinning of the contact line, leaving the non-wetting counterpart challenging due to the low liquid affinity. In this work, confinement is imposed on droplets located on well-designed shapes and arrangements of microtextured surfaces. An active way to shape non-wetting water and liquid metal droplets into various polygons ranging from triangles, squares, rectangles, to hexagons is developed. The results suggest that energy barriers in different directions account for the movement of the contact lines and the formation of polygonal shapes. By characterizing the curvature of the liquid-vapour meniscus, the morphology of the droplet is correlated to its volume, thickness, and contact angle. The developed liquid-based patterning strategy under active regulation with low adhesion looks promising for low-cost micromanufacturing technology, DNA microarrays, and digital lab-on-a-chip.


Supplementary Method 1. Experimental procedure
The experimental setup is shown in Supplementary Fig. 1a. Before the experiment was carried out, the setup was optimized to guarantee that the microtextured surface and the upper glass plate are parallel to each other. To realize this aim, the following procedures were carried out.
First, the platform with the sample was adjusted by using an air level. Then, five droplets were deposited at five different positions of the sample (i.e., the center, and another four locations which are close to the corners of the sample), and smoothly decline the upper plate to compress these droplets. Meanwhile, the base plate was controlled by a high precision motorized goniometer (x-Zolix PSAG15-250, y-Zolix PSAG15-370). The spreading behaviors of these five droplets were monitored. When all of them were able to achieve same spreading behaviors, the upper plate and the bottom sample were believed to be sufficiently parallel to each other.
After that, experiments and data recording data were carried out. was first deposited on the micropillared surfaces. Then, the superhydrophobic glass plate was used to press the big drop to make it in the Wenzel wetting state. After that, the upper glass plate was lifted up, and then a liquid metal droplet was deposited in the big drop and meanwhile on a b  Supplementary Fig. 1b. Since the intrinsic contact angle of the liquid metal droplet on the silicon surface in the H2SO4/water mixture environment was quite high (i.e., θ0 = 154.3 ± 1.6°), the liquid metal droplet was in the Cassie-Baxter wetting state. After these steps were finished, similar experimental procedures (for water droplets) were carried out for liquid metal droplets.
As shown in Supplementary Fig. 2, the top view of the microtextured surface employed in the experiments is shown. Specifically, Supplementary Fig. 2a demonstrates the triangular pillars arranged in hexagonal (circle 1), triangular (circle 2) and square (circles 3 and 4) arrays. The side length a of the pillar and the spacing b between the pillars are defined. As shown in Supplementary Fig. 2b-d, the appearances of the square, hexagonal and circular pillars arranged in various arrays are shown, respectively. In Supplementary Fig. 2c, a is defined as the distance between the two points on the diagonal of the hexagonal pillars. In Supplementary Fig. 2d, a is defined as the diameter of the circular pillars.

Supplementary Discussion 1. Solidification of the liquid film
Despite the reversibility and reproducibility of the wetting state, we are wondering whether the liquid pattern could be fixed when the confinement is released, which is challenging, but remains significant for potential applications in microfabrication. To check this point, more experiments were carried out. Different from the above tests, in this case, the experiment was carried out on a cold platform. As shown in Supplementary Fig. 3a, a square liquid metal (Galinstan) droplet was first obtained. Then, the temperature of the substrate was decreased to -20°C and kept for 20 min. During this period, solidification happens. After that, the upper glass plate was completely removed, and the square shape of the film was kept, as shown in Supplementary Fig. 3b. Moreover, when we used a needle to touch the square film, scratches appeared which suggests that the square film was fixed as a solid piece. In other words, the solidification of the polygonal liquid metal suggests our method would find applications in microfabrication. However, when making a comparison between Supplementary Figs. 3a and 3b, it is noted that the experimental process slightly affects the shape and size of the liquid film.
The deviation between the solidification and the original liquid film is still an interesting topic for further scrutiny.  Table   1).

b a
It is worth discussing the generality of our method to create polygonal patterns using other liquid metals. As shown in Supplementary Fig. 4, when we replaced the Galinstan droplet by a mercury droplet, a square liquid film was well formed.

Supplementary Discussion 3. Reversibility of the wetting state transition due to confinement
The reversibility of the wetting state transition of the polygonal droplets is checked in this section. Two examples of water and liquid metal droplets are presented in Supplementary Fig.   5a and b, respectively. The experimental processes are illustrated as follows. Before imposing confinement, the droplets were spherical (Supplementary Fig. 5(a-i) and (b-i)). Then, the upper superhydrophobic glass plate was lowered to force the spherical droplet to form polygonal patterns ( Supplementary Fig. 5(a-ii) and (b-ii)). After that, the confinement was smoothly removed, the droplet recovered a spherical shape, suggesting a robust reversibility of the wetting state transition. During these processes, the droplets always keep the Cassie-Baxter wetting state. Moreover, the reversibility of the wetting state is available for all the experiments presented in the paper. droplets. (a-i) After a water droplet was deposited on the substrate but before the confinement was imposed, the droplet demonstrated a spherical shape. (a-ii) A square liquid film was formed when the confinement was imposed. (a-iii) After the confinement was removed, the droplet recovered to a spherical shape. Scale bar, 500 μm. The sample is No. 12a in Supplementary Table 1

Supplementary Discussion 4. Reproducibility of the polygonal droplet pattern
The reproducibility of the wetting state is demonstrated as follows. As shown in Supplementary   Fig. 6, the morphologies of a water droplet are given. Specifically, the upper superhydrophobic glass plate was lowered to a certain height H (H > Hc) and then lifted, and the processes were repeated three times. Supplementary Fig. 6a However, the reproducibility of the wetting state of the liquid metal is not as good as water.
One possible reason is that the separation between the glass plate and the substrate in each confinement did not exactly have the same value. The liquid metal (Galinstan) has a much higher surfaces tension (624 mN/m) than water (72 mN/m), in order to create polygonal patterns, the liquid metal droplets have to be much highly confined compared with water droplets.
Optimization of the experimental setup will a much higher precision will be the objective of our future work.   The liquid volume conservation leads to the following relationship where V0 is the volume of the droplet. Thus, the length of E is obtained as m,2 0 2 m2 2 3 11 6 3 As shown in Fig. 5a of the main paper, the result of Eq. (4) (red curve) agree very well with the experimental data (black and red dots) with no adjustable parameter.
As shown in Fig. 5a  shapes, similar calculations can be carried out based on the above theoretical framework.

Supplementary Discussion 7. Spreading priority of the liquid
In addition to Fig. 6 in the main paper about the spreading priority of the contact line, as shown in Supplementary Fig. 10, more cases of the evolution of the droplet pattern are given. In Supplementary Fig. 10a, because the pillars arrange in the hexagonal pattern, when the droplet pattern is forming, the contact lines move synchronously (Supplementary Movie 5). However, as shown in Supplementary Fig. 10b, for the surface consisting of triangular pillars but arranged in the square pattern, when the square droplet pattern is forming, the four sides of the droplet

Supplementary Movie. Description of the Supplementary movie
All the movies were captured from the top view. The frame rate of the CCD camera is 30 frames per second (fps). When a droplet with a certain volume V0 was deposited on the substrate, it adopts a circular solid-liquid-vapor three-phase contact line and a certain height H0. After that, the superhydrophobic glass plate was smoothly declined to compress the droplet, and a polygonal droplet pattern appears. At the moment that the separation between the substrate and the glass plate reached a critical value Hc, the collapse happened. Detailed information of the movies is listed in Supplementary